More on the d7
Jul. 6th, 2007 03:21 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
jackhttp://hjem.get2net.dk/Klaudius/Dice.htm
http://homepage.ntlworld.com/dice-play/DicePolyMath.htm
*sigh* Googling has shown more. *Of course* dice don't have to be platonic, the desire is isohedral -- where each face is symmetric with each other face but there's no requirement that the vertices. That satisfies the "obviously fair by geometry without any messy dynamics" requirement.
The good news is, there's lots of lists of lots of dice shapes. The bad news is, none of them introduce any new factors, the only numbers producible[1] are still just multiples of 2,3 and 5.
[1] Without cheating and rolling a pencil-like object with seven stable faces. That obviously *works* but is so clearly unaesthetic.
ETA: But that doesn't close the door entirely, though hope seems unlikely. For instance, consider a pencil with seven sides, and at each end, a point in a heptagonal pyramid. That's polyhedral, and fair amongst the seven sides, it's just not very spherical. We haven't yet shown that you can't make a spherical thing the same way, though it seems unlikely, seven isn't good at factoring.
http://homepage.ntlworld.com/dice-play/DicePolyMath.htm
*sigh* Googling has shown more. *Of course* dice don't have to be platonic, the desire is isohedral -- where each face is symmetric with each other face but there's no requirement that the vertices. That satisfies the "obviously fair by geometry without any messy dynamics" requirement.
The good news is, there's lots of lists of lots of dice shapes. The bad news is, none of them introduce any new factors, the only numbers producible[1] are still just multiples of 2,3 and 5.
[1] Without cheating and rolling a pencil-like object with seven stable faces. That obviously *works* but is so clearly unaesthetic.
ETA: But that doesn't close the door entirely, though hope seems unlikely. For instance, consider a pencil with seven sides, and at each end, a point in a heptagonal pyramid. That's polyhedral, and fair amongst the seven sides, it's just not very spherical. We haven't yet shown that you can't make a spherical thing the same way, though it seems unlikely, seven isn't good at factoring.